Question: $\dfrac{ -9w - 7x }{ -10 } = \dfrac{ 2w - 6y }{ -7 }$ Solve for $w$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -9w - 7x }{ -{10} } = \dfrac{ 2w - 6y }{ -7 }$ $-{10} \cdot \dfrac{ -9w - 7x }{ -{10} } = -{10} \cdot \dfrac{ 2w - 6y }{ -7 }$ $-9w - 7x = -{10} \cdot \dfrac { 2w - 6y }{ -7 }$ Multiply both sides by the right denominator. $-9w - 7x = -10 \cdot \dfrac{ 2w - 6y }{ -{7} }$ $-{7} \cdot \left( -9w - 7x \right) = -{7} \cdot -10 \cdot \dfrac{ 2w - 6y }{ -{7} }$ $-{7} \cdot \left( -9w - 7x \right) = -10 \cdot \left( 2w - 6y \right)$ Distribute both sides $-{7} \cdot \left( -9w - 7x \right) = -{10} \cdot \left( 2w - 6y \right)$ ${63}w + {49}x = -{20}w + {60}y$ Combine $w$ terms on the left. ${63w} + 49x = -{20w} + 60y$ ${83w} + 49x = 60y$ Move the $x$ term to the right. $83w + {49x} = 60y$ $83w = 60y - {49x}$ Isolate $w$ by dividing both sides by its coefficient. ${83}w = 60y - 49x$ $w = \dfrac{ 60y - 49x }{ {83} }$